Donald Trump taketh back what he giveth ... he's back to saying there was violence in Charlottesville Saturday on both sides -- left and right.

The President faced reporters at Trump Tower in NYC Tuesday and blamed the "alt-left" as much as the alt-right for the violent showdown.

When he was confronted by a reporter, he hurled an insult and moved on.

Trump scored with one fan ...former KKK leader David Duke just tweeted, "Thank you President Trump for your honesty & courage to tell the truth about #Charlottesville and condemn the leftist terrorists in BLM/Antifa."